I don't know much about BaseCamp, but I suspect it is a web application. I see they're using BGP Anycast to serve to the closest location. I looked in their further article for more detail but there wasn't really much information, but how does BGP Anycast work with TCP? I'm guessing they're doing everything best effort and hoping that when a route is chosen between Chicago & Virginia, that the closest path is taken at all times and there's no path "jitter" between Chicago & Virginia, e.g. a SYN packet won't go to Chicago and the following SYN+ACK go to Virginia.
Anyone have any insights?